i'm not exactly sure about the first question, but I do know that we dont need to know it.
for your second question, V
out can be a combination of both (usually is), unless a capacitor is placed somewhere there (there's two positions to put it) which decouples it to only AC
peak-to-peak refers to twice the amplitude of the AC component. its basically

or can be written as

"disconnected" just refer to 0V from V
in, or basically just 0.7V going into V
band current gain is the current amplification, it depends on the transistor itself, it is

. Since I
CE is practically I
C, and I
BE is practically I
B, a current gain of 100 means an I
b of

will be amplified to

at R
CVoltage gain depends on the circuit configuration and the current gain, where

they are kind of related.... based on similar principles, but very different things.